Hilbert–Schmidt Frames: Duality, Weaving and Stability

Choubin, Mehdi; Ghaemi, Mohammadbagher; Kim, Gwang Hui

doi:10.22075/ijnaa.2020.4251

Hilbert–Schmidt Frames: Duality, Weaving and Stability

Document Type : Research Paper

Authors

Mehdi Choubin ¹

Mohammadbagher Ghaemi ²

Gwang Hui Kim ³

¹ Department of Mathematics, Velayat University, Iranshahr, Iran

² Department of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

³ Department of Mathematics, Kangnam University, Yongin, Gyeonggi, 16979, Republic of Korea

10.22075/ijnaa.2020.4251

Abstract

In this paper, we give some sufficient conditions under which perturbations preserve Hilbert-Schmidt frames. Also show that the canonical dual of a perturbed Hilbert-Schmidt frame is a perturbation of the canonical dual (alternative dual respectively) of the original Hilbert-Schmidt frame and discuss best approximation in the set of all dual Hilbert-Schmidt frames. Next, we apply the woven principle to Hilbert-Schmidt frames and study the stability of weaving Hilbert-Schmidt frames under perturbations. Finally, we present sufficient conditions under which perturbations preserve weaving Hilbert-Schmidt frames and weaving dual Hilbert-Schmidt frames.

Keywords

Hilbert-Schmidt frames

Weaving frames

Dual frames

Perturbation